Self-Organizing Maps, Principal Components and Non-negative ...
Self-Organizing Maps, Principal Components and Non-negative ...
Self-Organizing Maps, Principal Components and Non-negative ...
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<strong>Self</strong> <strong>Organizing</strong> <strong>Maps</strong><br />
<strong>Principal</strong> <strong>Components</strong>, Curves <strong>and</strong> Surfaces<br />
<strong>Non</strong>-<strong>negative</strong> Matrix Factorization<br />
<strong>Principal</strong> <strong>Components</strong><br />
<strong>Principal</strong> Curves<br />
Spectral Clustering<br />
This leaves us to find the orthogonal matrix Vq<br />
min<br />
Vq<br />
N<br />
(xi − ˆx) − VqV T q (xi − ˆx) 2<br />
i=1<br />
The projection matrix Hq = VqV T q maps each point xi onto<br />
its rank-q reconstruction Hqxi.<br />
Other expression of the solution, singular value decomposition<br />
X = UDV T<br />
X...the rows contain the centered observations<br />
(7)<br />
(8)<br />
Karoline Geissler <strong>Self</strong>-<strong>Organizing</strong> <strong>Maps</strong>, <strong>Principal</strong> <strong>Components</strong> <strong>and</strong> <strong>Non</strong>-<strong>negative</strong> M
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